Shaping optical elements that are not only aspherical but that are also of large dimensions is a process that is lengthy, difficult, and expensive because of the requirements in terms of accuracy and surface smoothness. A particularly advantageous method of proceeding is a method of polishing under stress that is known as “stressed mirror polishing (SMP)”. It is described in detail in the following articles:                “Stressed mirror polishing. 1: A technique for producing non-axisymmetric mirrors”, Jacob Lubliner and Jerry E. Nelson, Applied Optics, Vol. 19, Issue 14, pp. 2332-2340 (1980); and        “Stressed mirror polishing. 2: Fabrication of an off-axis section of a paraboloid”, Jacob Lubliner and Jerry E. Nelson, Applied Optics, Vol. 19, Issue 14, pp. 2341-2352 (1980).        
The general principle consists in machining a spherical structure on a stressed blank so as to obtain a surface that is aspherical once the stress is released. The intended purpose is to obtain an optical surface that is aspherical while performing the shaping on a surface that is spherical, because the tools used for shaping a spherical surface provide very high performance, in particular when shaping surfaces of items of large dimensions. Thus, a feature of polishing under stress is how to implement the stress.
In order to implement the method, an appropriate blank is generally in the form of a plate, i.e. with one of its dimensions that is significantly smaller (by one or more orders of magnitude) than its other two dimensions. Typically, the blank may have thickness of the order of 10 millimeters (mm) to 100 mm, e.g. 50 mm, and a diameter of the order of 1000 mm to 2000 mm, or even more. Thus, the plate has two faces, which are referred to as main surfaces, and a side surface.
One of the two main surfaces is the “optical” surface that needs to be shaped. Preferably, its original shape is spherical or planar. The term “blank” is used herein to mean the optical element in its state prior to being shaped under stress.
The other main surface of the blank is the rear surface behind the optical surface.
In the conventional SMP technique, radially-oriented arms are fastened to the side surface of the blank, e.g. by adhesive. In the above-mentioned articles by J. Lubliner et al., it is shown that deformation appropriate for the intended purpose can be obtained by subjecting said arms only to shear force that are oriented parallel to the surface.
As explained above, the forces applied to the blank are selected so as to give the optical surface a spherical shape complementary to the desired shape. The deformation (departure from a spherical shape) may reach values of several hundreds of micrometers; and it may be monitored accurately by performing interferometric measurements on the optical face itself or on the rear face of the blank.
Thereafter, a method of shaping by abrasion is performed in order to make the deformed surface planar or spherical. Finally, releasing the stresses allows the blank to relax, and the shaped surface takes on the desired aspherical shape.
That method suffers from imperfections. The forces and the moments are applied by means of arms, thereby giving rise to stresses at the periphery of the blank that are not uniform. On its outer perimeter, stress fluctuates between local maxima at the root end of each arm and local minima between arms. After shaping, this gives rise to serrations, i.e. undesirable geometrical modulation of the optical surface at the periodicity of the arms.
The method described in patent EP 2 144 093 remedies that unwanted effect by fastening a blank of an optical element having an optical surface that is to be shaped to a ring. FIGS. 1 and 2 show such fastening of the optical element 1 to the ring 2. FIG. 1 shows in particular a ring 2 of diameter dl that surrounds an optical element 1 and that is itself surrounded by a multitude of arms 4. It is these arms that apply the stress to the ring, which in turn stresses and deforms the optical element 1. The forces are thus applied by the arms to the perimeter 23 of the ring 2 in order to deform it in controlled manner, and also deform in controlled manner the optical element 1 that is fastened thereto, and thus deform its optical surface 10. That ring distributes the stresses uniformly within the optical part and makes it possible to avoid generating defects of high spatial frequency. Finally, the last step of the method consists in extracting the blank 1 from the ring 2 so as to release the stresses deforming said optical surface that has been shaped by abrasion in order to enable the surface to acquire the desired aspherical shape.
FIG. 2 shows more precisely the prior art method of fastening the optical element 1 to the ring 2. It consists in:                inserting the optical element 1 inside the ring 2: the outside surface 12 of the optical element faces the inside surface 33 of the ring; and        using a layer of adhesive 3 for fastening the optical element to the ring before applying stresses.        
That method presents the following drawbacks:                requiring a strict match between the size of the ring and the size of the blank;        making use of high levels of stress in the layer of adhesive; and        occupying a large amount of space around the completed assembly as a result of the presence of the arms.        